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Chapter 11: Problem 9

You are an executive for Super Computer, Inc. (SC), which rents out super computers. SC receives a fixed rental payment per time period in exchange for the right to unlimited computing at a rate of \(P\) cents per second. SC has two types of potential customers of equal number-10 businesses and 10 academic institutions. Each business customer has the demand function \(Q=10-P,\) where \(Q\) is in millions of seconds per month; each academic institution has the demand \(Q=8-P\). The marginal cost to \(\mathrm{SC}\) of additional computing is 2 cents per second, regardless of volume. a. Suppose that you could separate business and academic customers. What rental fee and usage fee would you charge each group? What would be your profits? b. Suppose you were unable to keep the two types of customers separate and charged a zero rental fee. What usage fee would maximize your profits? What would be your profits? c. Suppose you set up one two-part tariff-that is, you set one rental and one usage fee that both business and academic customers pay. What usage and rental fees would you set? What would be your profits? Explain why price would not be equal to marginal cost.

Short Answer

Expert verified
a. For business customers, the rental fee is 160 million cents and for academic institutions, it is 100 million cents. b. If we were unable to separate the two types of customers and charged a zero rental fee, we would charge a usage fee of 7 cents per second and get a profit of 140 million cents. c. With a two-part tariff, the usage fee would be set at 2 cents per second and the rental fee to obtain the consumer surplus, resulting in a total profit of 780 million cents. In this case, price is not equal to marginal cost because in two-part tariffs, firms can extract consumer surplus, resulting in higher prices.

Step by step solution

01

Determine optimal fees for business customers and academic institutions separately

Businesses: To find the optimal usage fee, we set the demand function equal to the marginal cost: \(10 - P = 2\), hence \(P = 8\). The total computing seconds demanded by every business is \(Q = 10 - P = 10 - 8 = 2\) million seconds. Multiply the usage price with the total quantity: Monthly revenue is \(2 * 8 = 16\) million cents. As there are 10 businesses, total business revenue is \(16 * 10 = 160\) million cents. Academic Institutions: Performing the same operation, we equate the demand function with marginal cost: \(8 - P = 2,\) then we find \(P = 6\). Following the same steps, we find the total revenue to be \(100\) million cents from academic institutions.
02

Determine usage fee when unable to separate customer types

Combining both customer types, we operate on the average of the two demand curves. Average demand is \((Q_1 + Q_2) / 2 = (10 - P + 8 - P) / 2 )\). Then we set this equal to the marginal cost, \(2\) which gives us \(P = 7\). The total revenue in this case is \(140\) million cents.
03

Determine the two-part tariff fee

For the two-part tariff case, the optimal per unit price is set at marginal cost: \(P = 2\) cents per second. The total seconds for each business are \(Q = 10 - 2 = 8\) million seconds. The revenue from each business is \(8 * 2 = 16\) million cents. The total seconds for each academic institution are \(Q = 8 - 2 = 6\) million seconds. The total usage revenue is \((16 * 10) + (6 * 2 * 10) = 280\) million cents. However, the price paid by customers is above the marginal cost, meaning there is consumer surplus. This surplus can be charged as a rental fee. For charging the rental fee, the consumer surplus should be calculated. This is defined as the area between the demand curve and the price, representing the extra worth each consumer receives above what they pay. The rental fee simply extracts this consumer surplus. Consumer surplus for businesses is \((1/2)*(10 - 2)*8 = 32\) million cents and for academic institutions, it is \((1/2)*(8 - 2)*6 =18\) million cents. Hence, adding all, the total profits would be \(280 + 320 + 180 = 780\) million cents.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Two-Part Tariff
In economics, the two-part tariff is a pricing strategy where customers are charged in two separate parts: a fixed fee and a variable usage fee. The aim of this strategy is to capture consumer surplus by setting a usage fee equal to the marginal cost and then charging an upfront fee that customers are willing to pay for the right to access the service.

For instance, in the case of Super Computer, Inc. (SC), the two-part tariff involves setting a rental fee (fixed part) and a per-second usage fee (variable part) for the usage of supercomputers. By setting the usage fee equal to the marginal cost of offering the service, 2 cents per second, SC can ensure they're covering their costs on the variable aspect of the service.

However, the key to maximizing profits lies in determining the rental fee, which is done by extracting the consumer surplus—the difference between what consumers are willing to pay and what they actually pay. By understanding the demand functions for business and academic customers, SC can optimize these fees to generate maximal revenue.
Marginal Cost Pricing
Marginal cost pricing is a method where the price for a good or service is set equal to the additional cost of producing one more unit of that good or service. This approach is central to competitive markets since it leads to efficient resource allocation.

Applying this to SC's strategy, the optimal per-unit price is the marginal cost of providing computing services, 2 cents per second. This price ensures that SC is meeting its production costs without necessarily including a markup. Marginal cost pricing helps avoid overproduction and underproduction, ultimately meeting the equilibrium between supply and demand.

However, when firms have the power to set prices, they may choose to deviate from marginal cost pricing to increase profits, as seen in the exercise where SC employs a two-part tariff to maximize revenue and profits.
Average Revenue
Average revenue (AR) is the revenue earned per unit of output sold and is found by dividing total revenue by the quantity sold. It's a crucial concept when assessing the profitability and pricing strategies of a company.

In the textbook solution, SC calculates AR when considering a pricing strategy that doesn't separate business and academic customers. AR helps SC in assessing the effectiveness of their pricing decisions. For instance, by setting a usage fee that brings the price to an average between the two groups, SC finds a position to unify demand and maximize profits across the customer base without differentiating pricing.
Demand Function
A demand function expresses the relationship between the quantity of a good or service demanded and its price. It's often used by businesses like SC to understand their consumers and to set prices accordingly.

The demand function can be represented mathematically, and for SC's customers, they are: for businesses, it is given by \(Q = 10 - P\), and for academic institutions, it is \(Q = 8 - P\). These functions express how demand varies inversely with price. By understanding and using demand functions, SC can make informed decisions about setting usage fees for different customer groups, as seen in the varying pricing structures discussed for business versus academic customers.

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Most popular questions from this chapter

Price discrimination requires the ability to sort customers and the ability to prevent arbitrage. Explain how the following can function as price discrimination schemes and discuss both sorting and arbitrage: a. Requiring airline travelers to spend at least one Saturday night away from home to qualify for a low fare. b. Insisting on delivering cement to buyers and basing prices on buyers' locations. c. Selling food processors along with coupons that can be sent to the manufacturer for a \(\$ 10\) rebate. d. Offering temporary price cuts on bathroom tissue. e. Charging high-income patients more than lowincome patients for plastic surgery.

Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to \(\$ 20,000\) and a fixed cost of \(\$ 10\) billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States, The demand for BMWs in each market is given by $$Q_{E}=4,000,000-100 P_{E}$$ and $$Q_{u}=1,000,000-20 P_{\mathrm{U}}$$ where the subscript \(E\) denotes Europe, the subscript \(u\) denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only. a. What quantity of BMWs should the firm sell in each market, and what should the price be in each market? What should the total profit be? b. If \(\mathrm{BMW}\) were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company's profit?

Elizabeth Airlines (EA) flies only one route: ChicagoHonolulu. The demand for each flight is \(Q=500-P\) EA's cost of running each flight is \(\$ 30,000\) plus \(\$ 100\) per passenger. a. What is the profit-maximizing price that EA will charge? How many people will be on each flight? What is EA's profit for each flight? b. EA learns that the fixed costs per flight are in fact \(\$ 41,000\) instead of \(\$ 30,000 .\) Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that EA faces, EA's average cost curve when fixed costs are \(\$ 30,000,\) and EA's average cost curve when fixed costs are \(\$ 41,000\) c. Wait! EA finds out that two different types of people fly to Honolulu. Type \(A\) consists of business people with a demand of \(Q_{\lambda}=260-0.4 P\). Type \(B\) consists of students whose total demand is \(Q_{\mathrm{B}}=240-0.6 P\) Because the students are easy to spot, EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does it charge other customers? How many of each type are on each flight? d. What would EA's profit be for each flight? Would the airline stay in business? Calculate the consumer surplus of each consumer group. What is the total consumer surplus? e. Before EA started price discriminating, how much consumer surplus was the Type \(A\) demand getting from air travel to Honolulu? Type \(B\) ? Why did total consumer surplus decline with price discrimination, even though total quantity sold remained unchanged?

A monopolist is deciding how to allocate output between two geographically separated markets (East Coast and Midwest), Demand and marginal revenue for the two markets are $$\begin{array}{ll}P_{1}=15-Q_{1} & \mathrm{MR}_{1}=15-2 Q_{1} \\ P_{2}=25-2 Q_{2} & \mathrm{MR}_{2}=25-4 Q_{2}\end{array}$$ The monopolist's total cost is \(C=5+3\left(Q_{1}+Q_{2}\right)\) What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions?

Many retail video stores offer two alternative plans for renting films: A two-part tariff: Pay an annual membership fee (e.g., \(\$ 40\) ) and then pay a small fee for the daily rental of each film (e.g., \(\$ 2\) per film per day). A straight rental fee: Pay no membership fee, but pay a higher daily rental fee (e.g., \$4 per film per day). What is the logic behind the two-part tariff in this case? Why offer the customer a choice of two plans rather than simply a two-part tariff?
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